1. Field
This invention is in the field of miniature rheometer or viscometer devices that measure true viscosity, elasticity, or flow rate of liquid.
2. State of the Art
Viscosity is a measure of resistance of liquid to flow and its value depends on the rate of deformation for Non-Newtonian liquids as described in Dynamics of Polymeric Liquids, Vol. 1, 1987 authored by R. B. Bird, R. C. Armstrong, and O. Hassager. The rate of deformation is given by a shear rate in a unit of (time)−1. The viscosity measured at a known shear rate is “true” viscosity. The dependence of the true viscosity on shear rate is a viscosity curve which characterizes material and is an important factor to consider for efficient processing. But in many cases viscosity is measured under ill-defined test condition so that shear rate can not be known or calculated. Under ill-defined conditions, the measured viscosity value is only “apparent”. Since the true viscosity is measured at a known shear rate, the true viscosity is universal whereas the apparent viscosity is not. Instead, the apparent viscosity depends on the measuring system. For example, as a common practice, a torque of a spindle immersed in a sea of test liquid is measured while the spindle is being rotated at a constant speed. In this case the torque value only yields an apparent viscosity since the shear rate is not known. At best, the apparent viscosity can be measured as a function of the rotational speed of the spindle. The rotational speed of the spindle can be in fact correlated with the shear rate only if a “constitutive equation” for the test liquid is known. However, a “constitutive equation” is seldom known for Non-Newtonian liquids. Therefore, true viscosity can not be measured with such ill-defined test condition for most non-Newtonian liquids.
The methods that give only apparent viscosities have been developed and used for quality controls in manufacturing and material characterization. Various on-line viscometers are designed for real time viscosity measurement. The prior art systems of U.S. Pat. No. 5,317,908 (Fitzgerald et al.) and U.S. Pat. No. 4,878,378 (Harada) are concerned with systems that measure apparent viscosities for process controls. The system of U.S. Pat. No. 6,393,898 describes a system that measures the apparent viscosities of many test liquids simultaneously. However, because of the non-universality of the apparent viscosity measurements obtained by these systems, a correlation of the apparent viscosity of a specific sample measured with a specific method with the true viscosity has to be found separately when desired. Fundamental development of formulations for materials requires the true viscosity measurement. Also the designs of processing equipment and accessories such as dies, molds, extrusion screws, etc., require the true viscosity of the material. However, the apparent viscosity measurement has been used for a quick test as an indication since it is easier and faster to measure and often more economical. The true viscosity is more difficult to get and can be only measured with a few types of instruments: rheometers and capillary viscometers. Rheometers impose a precise and known shear rate on test samples thereby measuring true viscosities. Rheometers are versatile and can be equipped to measure other properties also. Therefore they are usually expensive. Usually large amounts of sample are required for viscosity measurements with the prior art rheometers. Further, such rheometers are not well suited for on-line applications and for high throughput measurement. Circular capillary viscometers are another type of viscometer that can measure apparent and true viscosities depending on whether a proper compensation is taken into account. The capillary viscometer needs a pressure drop measurement along the capillary for viscosity. Since the capillary is circular, pressure at the entrance and exit can only be measured. Because of this limitation, the capillary viscometer measures only apparent viscosity unless the entrance effect is corrected for by using two different capillaries with different length to diameter ratios. However, use of two capillaries makes the viscometers bulky or time consuming. Examples of capillary viscometers can be found in prior art U.S. Pat. No. 6,575,019 (Larson), U.S. Pat. No. 4,920,787 (Dual et al.), U.S. Pat. No. 4,916,678 (Johnson et al.), and U.S. Pat. No. 4,793,174 (Yau).
Rectangular slit viscometers relevant to the current invention are also used to measure the true viscosity and such viscometers are well described in Rheology in Polymer Processing, 1976, authored by C. D. Han. In this viscometer, test liquid flows inside of a rectangular slit flow channel and local pressures along the flow channel are measured with deployed pressure sensors for a given flow rate. In contrast to the capillary viscometer, the inside of the slit flow channel is flat so that pressures in the slit flow channel can be measured with pressure sensors mounted in the slit flow channel. The positions of the pressure sensor have to be sufficiently inside of the slit flow channel so that pressures of a fully developed flow are measured. From the pressure measurement, wall shear stress can be calculated. As the flow rate is varied, shear rate can be varied. From the measurement of wall shear stress at different shear rates, true viscosities are calculated using the well known Weissenberg-Rabinowitsch correction, which is much simpler than using two separate capillaries in case of using circular capillary viscometers. These viscosity measurements, however, are only simpler if the width of the flow channel is sufficiently large compared to the depth of the flow channel. These slit viscometers need pumping systems for a precise control of volumetric flow rate of test liquid. Frequently, the slit viscometers are used as an attachment to extruders as the liquids flow out of the extruders. In current practices, the individual pressure sensors are mounted separately to the inside of the flow channels and must be mounted flush enough with the surface of the flow channel to measure unperturbed pressures. However, it is very well known that a perturbation of flow significantly influences pressure measurement in particular for viscoelastic non-Newtonian liquids. Also any slight surface roughness due to the mounting of pressure sensors may be a source of test sample deposition, which degrades long term performance let alone the difficulties of mounting individual pressure sensors. Therefore, the measurement accuracy is often compromised depending on how well the individual pressure sensors are mounted in the flow channel. With a single slit geometry, shear rate can only be changed by a change of volumetric flow rate controlled by the pumping system. Also, most current slit viscometers are made individually with conventional machining processes. In addition, all of these viscometers are made for relatively large samples. Therefore, relatively small sample sizes, such as micro sample sizes, cannot be measured with such systems. These conventional slit viscometers are not appropriate for measuring viscosities of test sample that are only available in a small quantity and for high throughput measurement.
For non-Newtonian liquids, flow elasticity is also a very important flow characteristic. The flow elasticity governs the flow in inkjetting, coating, spraying, etc. Therefore, measuring the flow elasticity is also an important characterization. Flow elasticity has been measured with rheometers, RFX opposed jet, Filament Stretching Extensional Rheometer (FISHER), Capillary Break-up Extensional Rheometer (CABER), Sudden Contraction flow Rheometers (Rodd, L. E., Scott, T. P., Boger, D. V., Cooper-White, J. J. and McKinley, G. H., Planar Entry Flow of Low Viscosity Elastic Fluids in Micro-Fabricated Geometries, J. Non-Newt. Fluid Mech. (2005), 129, 1-22), and converging flows rheometers (James, D. F., Flow in a Converging Channel at Moderate Reynolds Numbers, AIChE J., 1991, 37, 59-64). All these instruments are fairly large in size and are not suitable for high throughput measurement applications. The micro-fabricated planar entry flow by Rodd et al. is promising as the planar geometry is compact. However, the material used for the flow channel is soft rubber and hard to combine with sensor substrates.